Significant efforts were made to develop an integrated DC voltage reference insensitive to Process, Voltage and Temperature (PVT) variations. The DC voltage references are usually based on the Silicon bandgap. To create a DC current reference insensitive to PVT one need in theory just an integrated resistor insensitive to PVT. Unfortunately, integrated resistors are very sensitive to process variations and they drift with temperature. Clearly post fabrication control is needed to adjust the value of such a resistor.
The option of trimming the resistor post-fabrication does not resolve the temperature drift problem and one can trim only before packaging so the value of the current reference cannot be tuned post-trimming. It is true that if temperature drift is not a concern, trimming is a simple and robust solution. Trimming is done usually based on an external resistor. Using an integrated inductor reference could simplify the trimming process.
The option of using a resistor component external to the integrated circuit to set the current has at least the following disadvantages:
The external resistor requires additional pads.
The external resistor requires additional space on the integrated circuit support board i.e. printed circuit board.
The external resistor generates noise or picks up noise from the board and requires decoupling capacitors.
The external resistor value will drift with temperature.